Question

Integral of 1/((sinx)(1+sinx))​

Answer 1

Answer:

log |cosec x - cot x| - (tan x - sec x) + C

Step-by-step explanation:

Frame the integral as 1/(sinx) - 1/(1+sinx).

For the first part we use the formula for integral of cosecx i.e. log |cosecx - cotx|

For the second part, we multiply both the numerator and denominator with (1 - sinx). We divide the result further into (secx)^2 - secxtanx. This is easily integrable as tan x - sec x

Dont Forget the +C :|